LP solvable models for portfolio optimization: a classification and computational comparison

The Markowitz model of portfolio optimization quantifies the problem in a lucid form of only two criteria: the mean, representing the expected outcome, and the risk, a scalar measure of the variability of outcomes. The classical Markowitz model uses the variance as the risk measure, thus resulting in a quadratic optimization problem. Following Sharpe's work on linear approximation to the mean–variance model, many attempts have been made to linearize the portfolio optimization problem. There were introduced several alternative risk measures which are computationally attractive as (for discrete random variables) they result in solving linear programming (LP) problems. The LP solvability is very important for applications to real-life financial decisions where the constructed portfolios have to meet numerous side constraints and take into account transaction costs. The variety of LP solvable portfolio optimization models presented in the literature generates a need for their classification and comparison. It is the main goal of our work. The paper introduces a systematic overview of the LP solvable models with a wide discussion of their theoretical properties. This allows us to classify the models with respect to the types of risk or safety measures they use. The paper also provides the first complete computational comparison of the discussed models on real-life data.